I've been reading Capital off and on for months and this is a seemingly pretty important difference that I don't understand. Is there a difference between surplus labor and profit, and if so, what is it? Any explanations, links, or chapters in Capital I should check out are appreciated.
The rate of surplus-value does not necessarily correlate with the rate of profit.
The reason the rate of profit tends to fall is because constant capital (c) tends to increase its fraction of the total capital — the ratio c/v increases. This results from technological development reducing labor inputs over time.
But the rate of surplus-value s/v doesn't depend on constant capital at all. So if the rate of surplus-value tends to decrease, it can't be because of a change in the fraction of constant capital.
The rate of profit and the rate of surplus-value express different things.
The rate of profit is what motivates capitalists and the capitalist economy in general. A capitalist invests money M in order to receive M' > M at a later point. In developed capitalist society, this occurs with such regularity and uniformity that there emerges a "market rate" for this money growth, a singular rate of profit known to anyone who wishes to invest their money.
The rate of surplus-value — a category identified only through the chapter one analysis of value — is synonymous with rate of exploitation. It is a simple ratio of unpaid-to-paid labor, performed either by an individual worker or by the working class as a whole. In principle, this rate could stay fixed at 100% forever, and the rate of profit would decrease independently as c/v increases.